Digital signal processing techniques are used in many signal processing systems. Examples include image processing systems, radar and sonar systems, and digital communication systems. Any system in which digital computers, or digital hardware, or both are used to transmit, store, extract, enhance, code, decode, or filter signals containing information utilizes digital signal processing.
One class of signal processing techniques that is used in many of the above-mentioned systems is the class of ranked order filters. Ranked order operations offer robust performance in signal processing applications in any dimension. They are usually easy to implement and perform well in many situations in which linear filters fail. For instance, they very effectively reduce high frequency and impulsive noise in digital images without the extensive blurring and edge destruction associated with linear filters. Other successful applications of these filters include the smoothing of noisy pitch contours in speech signals, data compression in block truncation coding schemes, and speckle noise reduction in coherent imaging systems.
Perhaps the most familiar example of ranked order filtering operations is the use of the median filter. Investigations over the last few years have shown that this filter has many interesting properties. For instance, it has been shown that a median filter maps a class of one dimensional input signals into an associated set of root signals. Each of these root signals is by definition invariant to additional filter passes and is the result of repeated filter passes on one or more of the input signals. N. C. Gallagher and G. L. Wise, "A Theoretical Analysis Of The Properties Of Median Filters," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-29, pp. 1136-41 (December 1981).
Median filters are used, for example, in ultrasonic imaging systems (such as CAT-scanners), image processing systems, and image coding systems. They are used because they have been found to perform certain tasks, such as the removal of impulsive noise from data, both very well and very fast. However, regardless of how fast information processing devices, such as digital filters, can process information, it is always desirable for such devices to process information faster.
By improving the speed at which median filters can operate, systems in which they are currently used will be able to function much faster. For instance, CAT-scanners could produce the same quality images now produced, but in much shorter times. This would permit the machines to examine more patients each day, thus lowering the medical costs of the individual patients.